# C++ named requirements: RandomNumberEngine (since C++11)

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A random number engine is a function object returning unsigned integer values such that each value in the range of possible results has (ideally) equal probability.

Any random number engine is also a UniformRandomBitGenerator, and therefore may be plugged into any random number distribution in order to obtain a random number (formally, a random variate).

### Requirements

A type satisfies RandomNumberEngine if it satisfies UniformRandomBitGenerator and, given the following types and values, the semantic and complexity requirements in the table below are satisfied:

Type | Definition
`E` | a RandomNumberEngine type
`T` | `E::result_type`
Value | Definition
e | a value of type `E`
v | an lvalue of type `E`
x, y | values of type (possibly const-qualified) `E`
s | a value of type `T`
q | a SeedSequence lvalue
z | a value of type unsigned long long
os | an lvalue whose type is a specialization of std::basic_ostream
is | an lvalue whose type is a specialization of std::basic_istream
n | the size of `E`'s state
TA | the transition algorithm of `E`
GA | the generation algorithm of `E`

Expression | Return type | Semantics | Complexity
--- | --- | --- | ---
E() | N/A | Creates an engine with the same initial state as all other default-constructed engines of type `E`. | \(\scriptsize O(n)\)O(n)
E(x) | Creates an engine that compares equal to x. | \(\scriptsize O(n)\)O(n)
E(s) | Creates an engine whose initial state is determined by s. | \(\scriptsize O(n)\)O(n)
E(q) | Creates an engine whose initial state is determined by a single call to `q.generate`. | same as the complexity of `q.generate` called on a sequence whose length is n
e.seed() | void | Postcondition: e == E(). | same as E()
e.seed(s) | void | Postcondition: e == E(s). | same as E(s)
e.seed(q) | void | Postcondition: e == E(q). | same as E(q)
e() | `T` | Advances e’s state from `ei` to `ei+1` (i.e. TA(e `i`)) and returns GA(e `i`). | amortized constant
e.discard(z) | void | Advances e’s state from `ei` to `ei+z` by any means equivalent to z consecutive calls of e(). | no worse than the complexity of z consecutive calls of e()
x == y | bool | For all positive integer i, if the ith consecutive calls of x() and y() return the same value, returns true. Otherwise returns false. | \(\scriptsize O(n)\)O(n)
x != y | bool | !(x == y) | \(\scriptsize O(n)\)O(n)
os << x | decltype(os)& | With fmtflags set to std::ios_base::dec | std::ios_base::left and the fill character set to the space character, writes to os the textual representation of x's current state. Postcondition: os's fmtflags and the fill character are the same as before. | \(\scriptsize O(n)\)O(n)
is >> v | decltype(is)& | With fmtflags set to std::ios_base::dec, reads from is the textual representation of v's current state. If bad input is encountered, ensures that v’s state is unchanged by the operation and calls is.setstate(std::ios_base::failbit) (which may throw std::ios_base::failure). Precondition: is provides a textual representation that was previously written using an output stream pr satisfying all following conditions: is.getloc() == pr.getloc() is true. std::is_same<decltype(is)::char_type, `` decltype(pr)::char_type>::value is true. std::is_same<decltype(is)::traits_type, `` decltype(pr)::traits_type>::value is true. Postcondition: is's fmtflags are the same as before. | \(\scriptsize O(n)\)O(n)

### Standard library

The following standard library facilities satisfy RandomNumberEngine:

linear_congruential_engine (C++11) | implements linear congruential algorithm (class template)
mersenne_twister_engine (C++11) | implements Mersenne twister algorithm (class template)
subtract_with_carry_engine (C++11) | implements a subtract-with-carry (lagged Fibonacci) algorithm (class template)
philox_engine (C++26) | a counter-based parallelizable generator (class template)
discard_block_engine (C++11) | discards some output of a random number engine (class template)
independent_bits_engine (C++11) | packs the output of a random number engine into blocks of a specified number of bits (class template)
shuffle_order_engine (C++11) | delivers the output of a random number engine in a different order (class template)

The following standard library facilities satisfy UniformRandomBitGenerator but not RandomNumberEngine:

random_device (C++11) | non-deterministic random number generator using hardware entropy source (class)

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